So as owners and players and their legal counsel return to court-ordered mediation on Tuesday morning, the likelihood of the league giving ground in talks has clearly decreased.

With restlessness and uncertainty surrounding the NFL with the start of training camps a little more than two months away, the players could be in a tricky place.

DeMaurice Smith, the head of the NFL Players Association, sounded defiant outside the courthouse in Minneapolis on Monday despite the 2-1 decision from the three-judge panel of the 8th U.S. Circuit Court of Appeals.

“We’d like to make progress, but it’ll be hard to do. We have to wait to see what happens June 3,” Pittsburgh Steelers president Art Rooney II said earlier on his way into the federal courthouse for Monday’s mediation.

“We look forward to the argument. Look: This is something that the players are prepared for,” Smith said. “It’s a disappointment obviously, but as far as we can tell this is the first sports league in history who sued to not play its game. Congratulations.”

“We have an opportunity to resolve this matter and get the game back on the field, and that really should be our exclusive focus,” NFL lead negotiator Jeff Pash said.

Commissioner Roger Goodell, speaking to Buffalo Bills season ticket holders on a conference call, said he thinks there’s “still time” to strike a new collective bargaining agreement.

“But time is running short. It’s time to get back to the table and get those issues resolved,” Goodell said.

NFLPA president Kevin Mawae told The Associated Press he was disappointed with the 8th Circuit’s decision.

“The ruling in granting the stay of the injunction means that the NFL owners can continue to not let football be played,” he said.

The appellate court said it believes the NFL has proven it “likely will suffer some degree of irreparable harm without a stay.” The court also cast doubt on the conclusions of U.S. District Judge Susan Richard Nelson, who ruled April 25 that the lockout should be lifted to save the players from irreversible damage. The 8th Circuit panel put her decision on hold four days later, and this order was a more permanent stay of her ruling.

“Both sides raise valid points, and this is a case in which one party or the other likely will suffer some degree of irreparable harm no matter how this court resolves the motion for a stay pending appeal,” the majority wrote. “We do not agree, however, with the district court’s apparent view that the balance of the equities tilts heavily in favor of the Players. The district court gave little or no weight to the harm caused to the League by an injunction issued in the midst of an ongoing dispute over terms and conditions of employment.”

The appellate court said it would make its decision quickly, a “circumstance that should minimize harm to the players during the offseason and allow the case to be resolved well before the scheduled beginning of the 2011 season.”

The two sides met for more than eight hours before U.S. Magistrate Judge Arthur Boylan, the fifth day of mediation but the first since April 20. Neither side would elaborate on the discussions, citing the judge’s confidentiality order. Michael Hausfeld, an attorney for the retired players who joined the antitrust lawsuit against the league, said the players were reviewing a new proposal from the owners.

“It probably is not one that would be acceptable as is, but it clearly opens a dialogue,” Hausfeld said.

The 8th Circuit’s decision to keep the lockout in place could be a signal of how the two sides will fare in the full appeal. The majority opinion, from Judges Steven Colloton and Duane Benton, sided with the NFL. Judge Kermit Bye dissented in favor of the players.

“The district court reasoned that this case does not involve or grow out of a labor dispute because the players no longer are represented by a union,” the majority wrote. “We have considerable doubt about this interpretation.”

The 8th Circuit has been seen as a more conservative, business-friendly venue for the NFL than the federal courts in Minnesota. Colloton and Benton were both appointed by Republican President George W. Bush; Bye was appointed by President Clinton, a Democrat.

Bye dismissed the conclusions of his fellow judges, just as he did on April 29 in dissenting against a temporary stay. He didn’t buy the NFL’s argument that it would be unable to “unscramble the egg” — a reference to the chaos of handling player transactions with no CBA in place.

“The preliminary injunction does not dictate the NFL’s free agency rules, or any other conduct in general, outside of the lockout,” Bye said.

Still in the courts is a separate but related matter. U.S. District Judge David Doty is determining the fate of some $4 billion in broadcast revenue he previously ruled was unfairly secured by the NFL in the last round of contract extensions with the networks to use as leverage in the form of lockout insurance. The players have asked Doty to put that money in escrow and for more than $707 million in damages, too.

Goodell, Pash and four team owners — Rooney, Mike Brown of the Cincinnati Bengals, John Mara of the New York Giants and Jerry Richardson of the Carolina Panthers — were on hand with their legal team for Monday’s session with Boylan.

Smith and three other lawyers for the players were present for their side. Linebacker Ben Leber, one of the players listed as a plaintiff in the still-pending federal antitrust lawsuit against the league, also attended. Hall of Famer Carl Eller and attorneys were there representing the retired players.

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(TM and Copyright 2011 CBS Radio Inc. and its relevant subsidiaries. CBS RADIO and EYE Logo TM and Copyright 2011 CBS Broadcasting Inc. Used under license. All Rights Reserved. This material may not be published, broadcast, rewritten, or redistributed. The Associated Press contributed to this report.)